How to set up synchronization of sent gmail yandex emails?

Question

Email

Good afternoon.
There is a mailbox on GMail and one more on Yandex.
Mail comes to Yandex and from there is taken to GMail via pop3. Next, the letter is answered from the gmail window using the Yandex smtp server.
Question: why are there no emails sent via gmail (and corresponding Yandex smtp server) in the "sent" folder on Yandex? And, more importantly, how or what to do to make them appear there?
Thanks